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Several scientists created gas laws around the end of the 18th century. Each gas rule is identified by the names of the scientists who proposed it. As a result, we now identify the following five key gas laws. Boyle’s Law describes the link between a gas’s pressure and volume. The connection between the volume filled by a gas and its absolute temperature is given by Charles’ Law.
The connection between the pressure exerted by a gas on the walls of its container and the absolute temperature associated with the gas is described by Gay-Lussac’s law. The link between the volume occupied by a gas and the amount of gaseous material is given by Avogadro’s Law. By combining the preceding four rules presented by four different scientists, the Combined Gas Law, often known as the ideal gas law, may be created.
Statement of the Law
Boyle’s law describes the relationship between a gas’s pressure and volume at a constant temperature. The volume of a gas is inversely proportional to the pressure of a gas at a constant temperature.
The equation for Boyle’s law formula is:
V ∝ 1/P
Or
P ∝ 1/V
Or
PV = K1
V represents the gas volume, P represents the gas pressure, and K1 represents the constant. Boyle’s Law can be used to calculate the current pressure or volume of a gas and is also known as:
P1V1 = P2V2
Graphical Verification of Boyle’s Law
The connection between volume and pressure in a gas may be stated as Boyle’s law mathematically as follows (at constant mass and temperature).
P ∝ (1/V)
The pressure exerted by the gas is P, and the volume occupied by it is V. By adding a constant, k, to this proportionality, we can convert it into an equation.
P = k*(1/V) ⇒ PV = k
When the pressure exerted by the gas (P) is shown on the Y-axis, and the inverse of the volume occupied by the gas (1/V) is plotted on the X-axis, a straight line is formed.
Derivation and Boyle’s law formula
According to Boyle’s law, any change in the volume filled by a gas (at constant quantity and temperature) results in a difference in its pressure. Put another way, the product of a gas’s initial pressure and initial volume equals the product of the gas’s final pressure and final volume (at constant temperature and number of moles). This law can be mathematically represented as follows:
P1V1 = P2V2
Here,
P1 refers to the gas’s starting pressure.
V1 is the gas’s initial volume of occupancy.
P2 refers to the gas’s ultimate pressure.
The final volume filled by the gas is V2.
Boyle’s law formula suggests a pressure-volume connection, which may be used to get this phrase. PV = k for a certain quantity of gas at constant temperatures. Therefore,
P1V1 = k (initial pressure * initial volume)
P2V2 = k (final pressure * final volume)
∴ P1V1 = P2V2
When a gas’s container volume decreases, the equation can be used to predict the increase in pressure exerted by the gas on the container walls (and its quantity and absolute temperature remain unchanged).
Solved exercises on Boyle’s law
Exercise 1: When a human breathes, his lungs can contain up to 5.5 litres of air at 37°C body temperature and 1 atm = 101 kPa ambient pressure. The oxygen content of this air is 21%. Calculate how many oxygen molecules there are in the lungs.
Answer: The air inside the lungs can be treated as an ideal gas. The perfect gas law may be used to calculate the number of molecules.
PV = NkT
Here volume is given in the Litre. 1 Litre is volume occupied by a cube of 10 cm. 1 Litre = 10cm × 10cm × 10cm = 10-3 m3
N = PV/ kT
= 1.01× 105Pa × 5.5 × 10-3 m3 / 1.38× 10-23 JK-1× 310 K
= 1.29 × 1023 Molecules
Only 21% of nitrogen is oxygen. The total number of oxygen molecules in the atmosphere.
= 1.29 × 1023 × 21/100
The number of oxygen molecules is 2.7 × 1022 molecules.
Exercise 2: Calculate the volume of air in your classroom using NTP. Normal temperature (room temperature) and one atmospheric pressure are denoted as NTP.
Answer: A typical class is 6 metres long, 5 metres wide, and 4 metres tall. The room’s volume is V = 6 × 5 × 4 = 120m3. The number of moles may be determined. The volume of a gas occupied by any gas is equivalent to 24.6L at 300K room temperature.
The amount of moles is equal to
μ =120m3 / 24.6 x 10-3m3
≈ 4878 mol.
Air combines around 20% oxygen, 79% nitrogen, and 1% argon, hydrogen, helium, and xenon. Air has a molar mass of 29 g mol-1.
The total air mass in the room is thus m = 4878 × 29 = 141.4kg.
Conclusion
Boyle’s law only applies to ideal gases. The rule applies only at high temperatures and low pressures. At high pressures, the law breaks down. At high pressures, the ratio of pressure and volume does not remain constant but shows a slight rise. The volume growth is due to repelling interactions between molecules.
